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Properties

Label 3675.2.dq
Level $3675$
Weight $2$
Character orbit 3675.dq
Rep. character $\chi_{3675}(2,\cdot)$
Character field $\Q(\zeta_{420})$
Dimension $53376$
Sturm bound $1120$

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Defining parameters

Level: \( N \) \(=\) \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3675.dq (of order \(420\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3675 \)
Character field: \(\Q(\zeta_{420})\)
Sturm bound: \(1120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3675, [\chi])\).

Total New Old
Modular forms 54144 54144 0
Cusp forms 53376 53376 0
Eisenstein series 768 768 0

Trace form

\( 53376 q - 104 q^{3} - 260 q^{4} - 60 q^{6} - 196 q^{7} - 130 q^{9} + O(q^{10}) \) \( 53376 q - 104 q^{3} - 260 q^{4} - 60 q^{6} - 196 q^{7} - 130 q^{9} - 212 q^{10} - 112 q^{12} - 160 q^{13} - 68 q^{15} + 932 q^{16} - 40 q^{18} - 120 q^{19} - 72 q^{21} - 196 q^{22} - 208 q^{25} - 32 q^{27} - 184 q^{28} - 26 q^{30} - 72 q^{31} - 106 q^{33} - 200 q^{34} - 92 q^{36} - 208 q^{37} - 130 q^{39} - 220 q^{40} - 190 q^{42} - 128 q^{43} - 590 q^{45} - 156 q^{46} - 180 q^{48} - 208 q^{51} - 88 q^{52} - 130 q^{54} - 184 q^{55} + 48 q^{57} + 24 q^{58} - 108 q^{60} - 156 q^{61} - 98 q^{63} - 200 q^{64} - 54 q^{66} - 80 q^{67} - 240 q^{69} - 236 q^{70} - 76 q^{72} - 152 q^{73} - 100 q^{75} - 160 q^{76} - 148 q^{78} - 120 q^{79} - 78 q^{81} + 120 q^{82} + 600 q^{84} - 184 q^{85} - 148 q^{87} - 156 q^{88} + 60 q^{90} - 144 q^{91} + 66 q^{93} - 260 q^{94} - 54 q^{96} - 208 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3675, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.